Merge pull request #20 from Yuto-Yamamoto01/yyamamoto/chapter02

2章を追加

Author: taishi-n

yyamamoto/chapter02/q01.py

@@ -0,0 +1,17 @@
+import math
+
+def dft(x):
+    N = len(x)
+    X = [0] * N
+    for k in range(N):
+        for n in range(N):
+            X[k] += x[n] * math.exp(-1j*2*math.pi*k*n/N)
+    return X
+
+def idft(X):
+    N = len(X)
+    x = [0] * N
+    for n in range(N):
+        for k in range(N):
+            x[n] += X[k] * math.exp(1j*2*math.pi*k*n/N) / N
+    return x

yyamamoto/chapter02/q02.py

@@ -0,0 +1,23 @@
+import math
+import cmath
+
+def dft(x):
+    N = len(x)
+    X = [0] * N
+    for k in range(N):
+        for n in range(N):
+            X[k] += x[n] * cmath.exp(-1j*2*math.pi*k*n/N)
+    return X
+
+def idft(X):
+    N = len(X)
+    x = [0] * N
+    for n in range(N):
+        for k in range(N):
+            x[n] += X[k] * cmath.exp(1j*2*math.pi*k*n/N) / N
+    return x
+
+
+# ここからq02
+impulse = [1, 0, 0, 0, 0, 0, 0, 0]
+print(dft(impulse))

yyamamoto/chapter02/q03.py

@@ -0,0 +1,30 @@
+import math
+import cmath
+import matplotlib.pyplot as plt
+import numpy as np
+
+def dft(x):
+    N = len(x)
+    X = [0] * N
+    for k in range(N):
+        for n in range(N):
+            X[k] += x[n] * cmath.exp(-1j*2*math.pi*k*n/N)
+    return X
+
+def idft(X):
+    N = len(X)
+    x = [0] * N
+    for n in range(N):
+        for k in range(N):
+            x[n] += X[k] * cmath.exp(1j*2*math.pi*k*n/N) / N
+    return x
+
+impulse = [1, 0, 0, 0, 0, 0, 0, 0]
+dft_value = dft(impulse)
+
+# ここからq03
+idft_value = idft(dft_value)
+t = np.arange(0, 8, 1)
+fig = plt.figure()
+plt.plot(idft_value)
+fig.savefig('q03_graph')

yyamamoto/chapter02/q03_graph.png

@@ -0,0 +1,37 @@
+import math
+import cmath
+import numpy as np
+import matplotlib.pyplot as plt
+
+def dft(x):
+    N = len(x)
+    X = [0] * N
+    for k in range(N):
+        for n in range(N):
+            X[k] += x[n] * cmath.exp(-1j*2*math.pi*k*n/N)
+    return X
+
+def idft(X):
+    N = len(X)
+    x = [0] * N
+    for n in range(N):
+        for k in range(N):
+            x[n] += X[k] * cmath.exp(1j*2*math.pi*k*n/N) / N
+    return x
+
+
+# ここからq02
+impulse = [1, 0, 0, 0, 0, 0, 0, 0]
+dft_value = dft(impulse)
+
+A = 20 * np.log10(np.abs(dft_value))
+P = np.rad2deg(np.angle(dft_value))
+
+fig = plt.figure()
+fig.add_subplot(1, 2, 1)
+plt.plot(A)
+plt.title("Amplitude Spectrum")
+fig.add_subplot(1, 2, 2)
+plt.plot(P)
+plt.title("Phase Spectrum")
+fig.savefig('q04_graph')

yyamamoto/chapter02/q04.py

@@ -0,0 +1,29 @@
+import numpy as np
+import math
+import cmath
+
+def dft(x):
+    N = len(x)
+    X = [0] * N
+    for k in range(N):
+        for n in range(N):
+            X[k] += x[n] * cmath.exp(-1j*2*math.pi*k*n/N)
+    return X
+
+def idft(X):
+    N = len(X)
+    x = [0] * N
+    for n in range(N):
+        for k in range(N):
+            x[n] += X[k] * cmath.exp(1j*2*math.pi*k*n/N) / N
+    return x
+
+
+impulse = [1, 0, 0, 0, 0, 0, 0, 0]
+print(dft(impulse))
+
+
+# ここからq05
+print(np.fft.fft(impulse))
+
+# 同じ結果になった！！！！！

yyamamoto/chapter02/q04_graph.png

@@ -0,0 +1,30 @@
+import numpy as np
+import matplotlib.pyplot as plt
+
+A = 1       # 振幅
+f = 440     # 周波数 Hz
+sec = 3     # 信号長 s
+fs = 16000  # サンプリング周波数 Hz
+
+t = np.arange(0, sec, 1/fs) # サンプリング点の配列
+x = A * np.sin(2*np.pi*f*t) # 正弦波の値
+
+
+# ここからq06
+dft_value = np.fft.fft(x)
+A = 20 * np.log10(np.abs(dft_value))
+P = np.rad2deg(np.angle(dft_value))
+
+freq = fs * np.arange(len(A)) / len(A)
+# グラフの描画
+fig = plt.figure()
+fig.add_subplot(1,2,1)
+plt.plot(freq, A)
+plt.title('Amplitude spectrum')
+
+fig.add_subplot(1,2,2)
+plt.plot(freq, P)
+plt.title('Phase Spectrum')
+fig.savefig('q06_graph')
+
+

yyamamoto/chapter02/q05.py

@@ -0,0 +1,6 @@
+import numpy as np
+
+def Hamming(N):
+    n = np.arange(N)
+    w = 0.54 - 0.46 * np.cos(2*np.pi*n/(N-1))
+    return w

yyamamoto/chapter02/q06.py

@@ -0,0 +1,27 @@
+import numpy as np
+import matplotlib.pyplot as plt
+import math
+
+def Hamming(N):
+    n = np.arange(N)
+    w = 0.54 - 0.46 * np.cos(2*np.pi*n/(N-1))
+    return w
+
+A = 1       # 振幅
+f = 440     # 周波数 Hz
+sec = 3     # 信号長 s
+fs = 16000  # サンプリング周波数 Hz
+
+t = np.arange(0, sec, 1/fs) # サンプリング点の配列
+x = A * np.sin(2*np.pi*f*t) # 正弦波の値
+
+# ここからq08
+N = len(x)
+y = np.zeros(N)
+H = Hamming(N)
+y = x * H
+
+fig = plt.figure()
+plt.plot(t, y)
+fig.savefig('q08_graph')
+

yyamamoto/chapter02/q06_graph.png

@@ -0,0 +1,29 @@
+import numpy as np
+import matplotlib.pyplot as plt
+import math
+
+def Hamming(N):
+    n = np.arange(N)
+    w = 0.54 - 0.46 * np.cos(2*np.pi*n/(N-1))
+    return w
+
+# ここからq08
+N = 48000
+H = Hamming(N)
+dft_value = np.fft.fft(H)
+
+A = 20 * np.log10(np.abs(dft_value))
+P = np.rad2deg(np.angle(dft_value))
+
+fs = 16000
+freq = fs * np.arange(len(A)) / len(A)
+
+# グラフの描画
+fig = plt.figure()
+fig.add_subplot(1,2,1)
+plt.plot(freq, A)
+plt.title('Amplitude spectrum')
+fig.add_subplot(1,2,2)
+plt.plot(freq, P)
+plt.title('Phase Spectrum')
+fig.savefig('q09_graph')

yyamamoto/chapter02/q07.py

@@ -0,0 +1,59 @@
+import numpy as np
+import matplotlib.pyplot as plt
+import math
+import tqdm
+
+A = 1       # 振幅
+f = 440     # 周波数 Hz
+sec = 0.5     # 信号長 s
+fs = 16000  # サンプリング周波数 Hz
+
+t = np.arange(0, sec, 1/fs) # サンプリング点の配列
+x = A * np.sin(2*np.pi*f*t) # 正弦波の値
+
+X = np.fft.fft(x)
+
+def conv(x, h):
+    N = len(x)
+    n = np.arange(N)
+    z = np.zeros(N, dtype=complex)
+    for k in tqdm.tqdm(range(N)):
+        z[k] = np.sum(x[n] * h[k-n])
+    return z
+
+
+def Hamming(N):
+    n = np.arange(N)
+    w = np.zeros(N, dtype=complex)
+    w = 0.54 - 0.46 * np.cos(2*np.pi*n/(N-1))
+    return w
+
+N = len(x)
+y = np.zeros(N)
+H = Hamming(N)
+y = x * H
+
+# ここまでq08の内容
+
+
+N = 48000
+H = Hamming(N)
+Y = np.fft.fft(H)
+
+Z = np.zeros(N)
+Z = conv(X, Y) # np.convolve は巡回畳み込みをしないので使えませんでした...
+z = np.fft.ifft(Z)
+print(z)
+print(y)
+
+
+
+fig = plt.figure()
+fig.add_subplot(1,2,1)
+plt.plot(t, y)
+plt.title('q08')
+fig.add_subplot(1,2,2)
+plt.plot(t, z)
+plt.title('q10')
+fig.savefig('q10_graph')
+